LOCATE-A-QUAKE
Purpose
John J. Thomas
This is a simplified exercise that will let you and your students work with earthquakes the
way a seismologist (a person who studies earthquakes) would. You will be able to measure the
distance to an earthquake from three recording stations and locate it on a map. You can also learn
something about how their intensity shows on an earthquake recording.
Definitions
Earthquake - a sudden motion or trembling of the earth caused by the abrupt release of strain, which
has slowly accumulated in the earth. An earthquake is caused by a breaking of rocks and
we feel it as waves coming to us through the earth.
P-wave or primary wave - the earthquake wave that is a push-pull wave, alternating compression and
expansion in the direction in which the wave is moving. Its speed is 5.5-7.2 km/sec in the
crust of the earth so it is the first, or primary, wave to reach us. Take a Slinky and stretch it
between two people, bunch several coils at one end and them let them go. The wave moving
along the slinky is a P-wave. Sound is a P-wave.
S-wave or secondary wave - the earthquake wave that is a shake wave, the wave moves up and down
as it moves through the earth. Its speed is 3-4 km/sec in the crust of the earth, it is the
second wave to reach you. If you take a length of clothesline and stretch it loosely between
two people, one person shakes their end up and down. The wave moving along the rope is
an S-wave. A vibrating string on a violin is an S-wave.
Surface Wave - an earthquake wave that moves along the surface of the earth. These are much
slower than P- or S-waves. A good example of a surface wave would be an ocean wave.
The waves on a body of water move only along the surface.
Fault - a crack in the rocks of the earth. These cracks are caused by the rocks being bent until they
break. Like a stick, you can bend rocks a lot before they break. The bending, or strain,
builds up over time and then the rock cracks. If the rock has broken once, it can break again
along the same fault. Because the surface of the fault is rough and the rock is pressed
together by a lot of pressure, a long build-up of strain occurs before the rock breaks again
and the break can be violent.
Seismograph - an instrument for measuring earthquakes. It makes a graph (seismogram) of the
motion of the earth as it is recorded at the seismograph station, figure 1.
Epicenter - the location of the earthquake.
Figure 1. Seismograph
Teacher Information
The oldest known geologic instrument is a form of a seismograph. It consisted of a large
bronze pot with frog sculptures around the lip. In the mouth of each frog was a delicately balanced
ball. When an earthquake occurred, the jar would shake and the ball would fall out of the mouth of
the frog nearest the direction of the epicenter.
A seismograph is a very simple device, see figure 1. The main part is a large mass hung on
a rod at the end of a pivot like a pendulum. A large mass is used so that the pendulum has a large
inertia, or resistance to movement. When an earthquake occurs, the earth moves, but the pendulum,
because of its inertia, stays still. If you put a pen on the bottom of the pendulum just touching a
piece of paper, the earth will move the piece of paper as it moves during the earthquake and the pen
will make a line. Move the paper and you will have a seismogram, or a tracing of the movement of
the earth under the inertia pendulum. The paper is usually mounted on a rotating drum. Modern
seismographs are much more sophisticated, but consist of the same basic parts. The movement of
the earth under the pendulum is now amplified electronically and electricity makes the pen move
that draws a trace of the earthquake on a drum (see figure 1). In the most sophisticated
seismographs, all the earth movements are measured electronically, and then stored, analyzed, and
printed by computer.
The size of the wiggly trace on the seismograph is directly related to the size of the earthquake
and inversely related to the distance to the epicenter. Remember that the P-wave travels faster than
the S-wave. The earth is always vibrating, so a seismogram always shows a wiggly line even when
there are no earthquakes. When an earthquake occurs the wiggles become noticeably bigger (figure
2). The P-wave is always the first noticeably larger trace on the seismogram. Then the trace relaxes
to the normal earth vibrations. The S-wave is always the second noticeably larger trace. The
distance between these two traces on the seismogram is the difference in the time of arrival of the Pand the S-wave. Since we know the speed of the two waves, the distance between the P and the S is
a measure of the distance to the epicenter of the earthquake:
The P-wave travels at 6 km/sec and the S-wave at 3 km\sec. These would be average speeds
for waves in a granite.
The difference between the velocity of the P- and S-waves = 3 km.
Each inch on the seismogram is one minute.
The distance between the P-wave and the S-wave measured on the seismogram is six inches.
6 inches = 360 seconds.
The distance to the epicenter is 3 km X 360 seconds = 1080 km.
This is only distance, the earthquake could be in any direction. So the distance to the earthquake
would have to be drawn as a circle with a diameter equal to 1080 km around the location of our
seismograph. To locate the earthquake, we need three seismographs, preferably in a triangle around
the earthquake, to locate the earthquake. The following exercise will show how to locate an
earthquake and why we need three seismographs.
Equipment
Figures 2 and 3
A ruler
A circle drawing compass or a pencil with a string tied around it to act as a compass.
Student Activity
You may use the following instructions to do this exercise with your class or let the students use the
Worksheet on the following page.
1) Figure 2 shows four seismograms of the same earthquake measured at four different cities. The
students should first measure the distance between the P- and S- waves on each of the
seismograms. By using the scale at the bottom of the figure, they can translate this distance into
miles. Notice that the further the seismograph is from the epicenter, the later the P-wave arrives and
the longer the separation between the P- and S-waves.
2) Using the measurements from #1 and the scale on Figure 3, set the compass for the distance
between the P- and S-waves on the seismogram for any of the cities. With the point of the compass
at the city, draw a circle around the city. Now take a second city, and repeat the process. Notice that
the circles intersect at two points. This is why you need a third city.
3) Choose a third city that will make a triangle with the other two. Repeat the process of measuring
and drawing the circle and the three circles will intersect at only one point. You have now located the
earthquake! Depending on the accuracy of your measurements, the intersection will probably be a
small triangle. This used to be called the triangle of error, but is not known to be related to the depth
of the earthquake. If you used both Buffalo and Boston, your accuracy will normally not be as
good as if you had substituted Montreal or New York for one of them.
You can get a very sophisticated exercise in locating earthquakes called Virtual Earthquake by going
to:
http://www.sciencecourseware.com
This is an excellent exercise, but is for the more advanced student.
WORKSHEET
John J. Thomas
1) A seismograph is an instrument for measuring earthquakes. Look a figure 1. The heavy weight
does not move during an earthquake, but the earth does. The rotating drum moves with the earth.
Draw the kind of line that you think the pen would make when an earthquake shakes the earth
under the heavy weight.
Figure 1. Seismograph
2) Figure 2 shows four seismograms recorded at four different cities. The P-wave (shown as P on
the seismograms) is the fastest traveling wave and arrives at the seismograph first. The S-wave
(shown as S) is a little bit slower.
The seismograph station nearest the earthquake will receive the P-wave first and will have
the shortest distance between the P- and S-waves.
Which city is closest to the earthquake? _____________
Which is farthest? _________________
3) The distance between the P-wave and the S-wave is the distance of the earthquake from the
seismograph. Using a ruler and the distance scale at the bottom of the figure 2, measure the
distances from the earthquake to each of the cities.
Boston ____________ miles
Buffalo ____________ miles
Montreal ____________ miles
New York ____________ miles
Figure 2. Seismograms for Locate-a-Quake
4) Do the following exercise using figure 3 as your base map and figure 2 as your data.
On the scale on figure 3, set the point of your compass on zero and the point at the correct
distance. Without changing this distance, pick up the compass and put the point on the dot
for Boston and draw a circle around Boston. The seismogram only gives us distance, not
direction. That is why you draw the distance as a circle.
Figure 3. Base map for Locate-a-Quake
Do the same thing for Montreal. Notice that the two circles cross at two points. You are still
not sure which of these two points is the location of the earthquake. You need a third
seismogram.
The best arrangement for the seismograms is in a triangle around the earthquake. The worst
is a straight, or nearly straight, line through the earthquake. The best city for the third
seismogram would be:
_____________________
Choose your third city, set your compass at the right distance, and draw your third circle on
figure 3. There is only one place that all three circles meet. This is the location of the
earthquake! Depending on the accuracy of your measurements, the intersection will
probably be a small triangle. This used to be called the triangle of error, but is not known to
be related to the depth of the earthquake. The earthquake was at Blue Mountain Lake NY
and had an intensity of 3.5. It occurred at night. We felt the earthquake in Saratoga Springs
as a shaking and rattling of our bed and the entire house. One of my students was in bed in
a cabin 50 feet from the epicenter and she was tossed right out of bed onto the floor.
ANSWER SHEET – WORKSHEET
John J. Thomas
1) A seismograph is an instrument for measuring earthquakes. Look a figure 1. The heavy weight
does not move during an earthquake, but the earth does. The rotating drum moves with the earth.
Draw the kind of line that you think the pen would make when an earthquake shakes the earth
under the heavy weight.
The correct answer can be any wiggly line it does not have to be as complex as this.
2) Figure 2 shows four seismograms recorded at four different cities. The P-wave (shown as P on
the seismograms) is the fastest traveling wave and arrives at the seismograph first. The S-wave
(shown as S) is a little bit slower.
The seismograph station nearest the earthquake will receive the P-wave first and will have
the shortest distance between the P- and S-waves.
Which city is closest to the earthquake? ___Montreal___
Which is farthest? ___Buffalo_____
3) The distance between the P-wave and the S-wave is the distance of the earthquake from the
seismograph. Using a ruler and the distance scale at the bottom of the figure 2, measure the
distances from the earthquake to each of the cities.
Boston ___192______ miles.
Buffalo ___207______ miles.
Montreal ___120______ miles.
New York ___200______ miles.
4) Do the following exercise using figure 3 as your base map and figure 2 as your data.
On the scale on figure 3, set the point of your compass on zero and the point at the correct
distance. Without changing this distance, pick up the compass and put the point on the dot
for Boston and draw a circle around Boston. The seismogram only gives us distance, not
direction. That is why you draw the distance as a circle.
Do the same thing for Montreal. Notice that the two circles cross at two points. You are still
not sure which of these two points is the location of the earthquake. You need a third
seismogram.
The best arrangement for the seismograms is in a triangle around the earthquake. The worst
is a straight, or nearly straight, line through the earthquake. The best city for the third
seismogram would be:
___New York______
Choose your third city, set your compass at the right distance, and draw your third circle on
figure 3. There is only one place that all three circles meet. This is the location of the
earthquake! Depending on the accuracy of your measurements, the intersection will
probably be a small triangle. This used to be called the triangle of error, but is not known to
be related to the depth of the earthquake. The earthquake was at Blue Mountain Lake NY
and had an intensity of 3.5. It occurred at night. We felt the earthquake in Saratoga Springs
as a shaking and rattling of our bed and the entire house. One of my students was in bed in
a cabin 50 feet from the epicenter and she was tossed right out of bed onto the floor.